Precalculus: Mathematics for Calculus, 7th Edition

by
Stewart, James; Redlin, Lothar; Watson, Saleem

Answer

$\frac{c}{c-2}$

Work Step by Step

Looking at the denominator of the fraction:
Find the LCD (i.e. $c-1$) and adjust the $1$ accordingly.
This then becomes: $\frac{c-2}{c-1}$
Looking at the numerator of the fraction:
Find the LCD (i.e. $c-1$) and adjust the $1$ accordingly.
This then becomes: $\frac{c}{c-1}$
So the fraction is now:
$=\frac{\frac{c}{c-1}}{\frac{c-2}{c-1}}$
Flip the denominator and multiply:
$=\frac{c}{c-1}\times\frac{c-1}{c-2}$
Cancel out any common factors:
$=\frac{c}{1}\times\frac{1}{c-2}$
Multiply the two fractions:
$=\frac{c}{c-2}$